Abstract

The analytical expressions for the cross-spectral density function of partially coherent sinh-Gaussian (ShG) vortex beams propagating through free space and non-Kolmogorov atmospheric turbulence are derived, and used to study the classification of coherent vortices creation and distance of topological charge conservation. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale of turbulence and spatial correlation length, the distance of topological charge conservation will decrease, whereas the outer scale of turbulence and the Sh-part parameter have no effect on the distance of topological charge conservation. According to the creation, the coherent vortices are grouped into three classes: the first is the inherent coherent vortices of the vortex beams, the second is created by the vortex beams when propagating through free space, and the third is created by the atmospheric turbulence inducing the vortex beams.

© 2015 Optical Society of America

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References

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2013 (2)

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

O. Korotkova and E. Shchepakina, “Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere,” J. Opt. 15(7), 075714 (2013).
[Crossref]

2012 (2)

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

G. Zhou, Y. Cai, and X. Chu, “Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere,” Opt. Express 20(9), 9897–9910 (2012).
[PubMed]

2011 (2)

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).
[Crossref] [PubMed]

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

2010 (2)

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

2009 (2)

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (3)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

2006 (1)

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

2005 (2)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250(4-6), 218–230 (2005).
[Crossref]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

2001 (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

1997 (1)

1994 (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

1989 (1)

M. Zahid and M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70(5), 361–364 (1989).
[Crossref]

1979 (2)

Agrawal, A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[Crossref] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Anderson, I. M.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Bastiaans, M.

Bergman, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Cai, Y.

Carozzi, T. D.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Chen, Z.

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

Chu, X.

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Dholakia, K.

Ding, P.

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

Dipankar, A.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Dong, Y.

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Flossmann, F.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250(4-6), 218–230 (2005).
[Crossref]

Freund, I.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Gbur, G.

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008).
[Crossref] [PubMed]

Gu, Y.

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Herzing, A. A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Ibragimov, N. H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Istomin, Y. N.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Khamitova, R.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Korotkova, O.

O. Korotkova and E. Shchepakina, “Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere,” J. Opt. 15(7), 075714 (2013).
[Crossref]

Lezec, H. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Li, C.

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

Li, J.

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Li, A. Yang, and B. Lü, “Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence,” J. Opt. Soc. Am. A 25(11), 2670–2679 (2008).
[PubMed]

Li, X.

Liu, X.

Lü, B.

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Li, A. Yang, and B. Lü, “Comparative study of the beam-width spreading of partially coherent Hermite-sinh-Gaussian beams in atmospheric turbulence,” J. Opt. Soc. Am. A 25(11), 2670–2679 (2008).
[PubMed]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

Maier, M.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250(4-6), 218–230 (2005).
[Crossref]

Marchiano, R.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

McClelland, J. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

McMorran, B. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[Crossref] [PubMed]

Palmer, K.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Plonus, M. A.

Pu, J.

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19(27), 26444–26450 (2011).
[Crossref] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Sagaut, P.

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Schattschneider, P.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250(4-6), 218–230 (2005).
[Crossref]

Shchepakina, E.

O. Korotkova and E. Shchepakina, “Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere,” J. Opt. 15(7), 075714 (2013).
[Crossref]

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Simpson, N. B.

Sjöholm, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Tang, H.

Then, H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Thidé, B.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

Tian, H.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Tyson, R. K.

Unguris, J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Verbeeck, J.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Wang, S. C. H.

Yang, A.

Yang, Y.

Zahid, M.

M. Zahid and M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70(5), 361–364 (1989).
[Crossref]

Zhao, C.

Zhao, D.

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

Zheng, X.

Zhou, G.

Zhu, K.

Zubairy, M. S.

M. Zahid and M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70(5), 361–364 (1989).
[Crossref]

Appl. Phys. B (1)

Z. Chen, C. Li, P. Ding, J. Pu, and D. Zhao, “Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence,” Appl. Phys. B 107(2), 469–472 (2012).
[Crossref]

J. Opt. (1)

O. Korotkova and E. Shchepakina, “Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere,” J. Opt. 15(7), 075714 (2013).
[Crossref]

J. Opt. A (1)

J. Li and B. Lü, “Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices,” J. Opt. A 11(4), 045710 (2009).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Nature (1)

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref] [PubMed]

Opt. Commun. (3)

Y. Gu and G. Gbur, “Measurement of atmospheric turbulence strength by vortex beam,” Opt. Commun. 283(7), 1209–1212 (2010).
[Crossref]

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250(4-6), 218–230 (2005).
[Crossref]

M. Zahid and M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70(5), 361–364 (1989).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50(6), 5164–5172 (1994).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Dipankar, R. Marchiano, and P. Sagaut, “Trajectory of an optical vortex in atmospheric turbulence,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046609 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[Crossref] [PubMed]

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Proc. SPIE (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Scintillation index of optical plane wave propagating through non-Kolmogorov moderate-strong turbulence,” Proc. SPIE 6747, 67470B (2007).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non Kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Science (1)

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref] [PubMed]

Other (3)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

I. S. Gradshteyn, I. M. Ryzhik, A. Jeffrey, and D. Zwillinger, Table of Integrals, Series, and Products (Elsevier, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (4)

Fig. 1
Fig. 1 Position of coherent vortices of partially coherent ShG vortex beams propagating through (a)-(b) free space and (c)-(d) non-Kolmogorov atmospheric turbulence, ‘●’ m = + 1 and ‘○’m = −1. The illustrations give the contour lines of phase which correspond to the coherent vortices.
Fig. 2
Fig. 2 The position of coherent vortices of partially coherent ShG vortex beams propagating through non-Kolmogorov atmospheric turbulence for C ˜ n 2 = 10−13m-2/3.
Fig. 3
Fig. 3 The distance zc of topological charge conservation versus (a) the general structure constant C ˜ n 2 , (b) the general exponenta α, (c) the inner scale of turbulence l0 and (d) the outer scale of turbulence L0.
Fig. 4
Fig. 4 The distance zc of topological charge conservation versus (a) the spatial correlation length σ0, (b) the waist width w0, and (c) the Sh-part parameters Ω0.

Equations (32)

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E(s,z=0)=u(s) [ s x +isgn(m) s y ] | m | ,
sgn(m)={ 1, 0, 1, m>0, m=0, m<0,
E(s,0)=sinh[ Ω 0 ( s x + s y )]exp( s x 2 + s y 2 w 0 2 ) [ s x +isgn(m) s y ] |m| ,
W 0 ( s 1 , s 2 ,0)=[ s 1x s 2x + s 1y s 2y ±i( s 1x s 2y s 2x s 1y ) ]exp( s 1 2 + s 2 2 w 0 2 ) ×sinh[ Ω 0 ( s 1x + s 1y ) ]sinh[ Ω 0 ( s 2x + s 2y ) ]exp( ( s 1 s 2 ) 2 2 σ 0 2 ),
W( ρ 1 , ρ 2 ,z )= ( k 2zπ ) 2 d 2 s 1 d 2 s 2 W 0 ( s 1 , s 2 ,0 ) exp{ ik 2z [ ( ρ 1 s 1 ) 2 ( ρ 2 s 2 ) 2 ] } ×exp[ ψ ( s 1 , ρ 1 )+ψ( s 2 , ρ 2 )],
exp[ ψ ( s 1 , ρ 1 )+ψ( s 2 , ρ 2 )] =exp{4 π 2 k 2 z 0 1 0 dκdξκ Φ n ( κ,α )[1 J 0 ( k| ( 1ξ )( ρ 1 ρ 2 )+ξ( s 1 s 2 ) | )] } =exp{T( α,z )[ ( ρ 1 ρ 2 ) 2 +( ρ 1 ρ 2 )( s 1 s 2 )+ ( s 1 s 2 ) 2 ]},
T( α,z )= π 2 k 2 z 3 0 κ 3 Φ n ( κ,α )dκ,
Φ n (κ)=A(α) C ˜ n 2 exp[( κ 2 / κ m 2 )] ( κ 2 + κ 0 2 ) α/2 , (0κ,3<α<4),
A(α)= Γ(α1)cos( απ /2 ) / (4 π 2 ) ,
κ 0 = 2π / L 0 ,
κ m = {Γ[ (5α) /2 ]A( α ) 2π /3 } 1/( α5 ) / l 0 ,
T(α,z)= π 2 k 2 z 6( α2 ) A( α ) C ˜ n 2 { exp( κ 0 2 κ m 2 ) κ m ( 2α ) ×[ ( α2 ) κ m 2 +2 κ 0 2 ]Γ( 2 α 2 , κ 0 2 κ m 2 )2 κ 0 4α },
exp( p x 2 +2qx ) dx= π p exp( q 2 p ),
xexp( p x 2 +2qx ) dx= π p ( q p )exp( q 2 p ),
x 2 exp( p x 2 +2qx ) dx= 1 2p π p ( 1+ 2 q 2 p )exp( q 2 p ),
W( ρ 1 , ρ 2 ,z )= k 2 16AC z 2 exp[ ik 2z ( ρ 1 2 ρ 2 2 ) ]exp[T(α,z) ( ρ 1 ρ 2 ) 2 ] ×( M 1 + M 2 M 3 M 4 ),
M 1 =( E x 2 + E y 2 C 2 + 1 C I x 2 + I y 2 4 H 2 1 4H ±i I x E y E x I y CH )exp( B x 2 + B y 2 4A + E x 2 + E y 2 C ),
M 3 =( G x 2 + G y 2 C 2 + 1 C J x 2 + J y 2 4 H 2 1 4H ±i J x G y G x J y CH )exp( F x 2 + F y 2 4A + G x 2 + G y 2 C ),
A= 1 2 w 0 2 + 1 2 σ 0 2 +T(α,z),
B x = ik 2z ( ρ 1x + ρ 2x )T(α,z)( ρ 1x ρ 2x ),
C= 2 w 0 2 + k 2 4A z 2 ,
D x = ik z ( ρ 1x ρ 2x )+2 Ω 0 ,
E x = 1 2 ( D x ik 2Az B x ),
F x = B x + Ω 0 ,
G x = 1 2 [ ik z ( ρ 1x ρ 2x ) ik F x 2Az ],
H=A+ k 2 w 0 2 8 z 2 ,
I x = 1 2 ( B x ik w 0 2 D x 4z ),
J x = 1 2 [ F x + k 2 w 0 2 ( ρ 1x ρ 2x ) 4 z 2 ].
W free ( ρ 1 , ρ 2 ,z )= k 2 16 A 0 C 0 z 2 exp[ ik 2z ( ρ 1 2 ρ 2 2 ) ]( M 10 + M 20 M 30 M 40 ),
μ( ρ 1 , ρ 2 ,z)= W( ρ 1 , ρ 2 ,z) [ I( ρ 1 ,z)I( ρ 2 ,z) ] 1/2 ,
Re[ μ( ρ 1 , ρ 2 ,z) ]=0,
Im[ μ( ρ 1 , ρ 2 ,z) ]=0,

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